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There has been no shortage of things to talk about when it comes to Call Me by Your Name, the gorgeous swoon of a romance that, after debuting to a standing ovation at the Sundance Film Festival 10 months ago, finally hit theaters over the weekend to rave reviews.

Based on André Aciman’s novel of the same name, Luca Guadagnino’s film depicts the simultaneously sweet and carnal romance between 17-year-old Elio (Timothée Chalamet) and a 24-year-old grad student named Oliver (Armie Hammer), who stays with Elio’s family at an Italian villa for one sweat- and passion-soaked summer in the late ’80s.

But for all the talk of sex and love and masturbating with orchard fruits, there’s another moment in the film that anyone who sees it can’t stop talking about. It’s a scene that, for the intense connection between Elio and Oliver, is actually the lynchpin that makes this love story so powerful, and so affecting.

Delivered by Michael Stuhlbarg, who plays Elio’s father, it’s an emotional monologue about unconditional love and acceptance that is making audiences weep, and could very well win the veteran actor (A Serious Man, Steve Jobs, FX’s Fargo) the Best Supporting Actor Oscar.

Stuhlbarg is in a rare, if not historic, position, in which he has significant supporting roles in three predicted Best Picture frontrunners—The Shape of Water, The Post, Call Me by Your Name—but it’s his role in the latter, with a monologue that might just be the best of the year, that is garnering him some of the year’s biggest accolades.

(Light spoilers follow.)

The speech comes just as the film is nearly over. Elio is nursing his heartbreak after Oliver heads back to the U.S. at the summer’s conclusion, and his father, Mr. Perlman (Stuhlbarg), the professor Oliver had been studying with, calls him over for a conversation on the couch.

Without making assumptions, without making Elio uncomfortable, and without overstepping his bounds, Mr. Perlman tells Elio that he noticed the intense connection he had with Oliver. He doesn’t judge. In fact, he wants to make it clear that he accepts it. That he encourages it. That he may even be jealous that Elio has been able to find someone to feel so intensely about, regardless of gender. And remember folks, this is the ’80s!

“You had a beautiful friendship,” Mr. Perlman tells Elio. “Maybe more than a friendship. And I envy you.” (What follows is the speech’s text as it is in Aciman’s book, which nearly exactly mirrors the speech in Guadagnino’s film.)

“In my place, most parents would hope the whole thing goes away, or pray that their sons land on their feet soon enough,” Mr. Perlman says. “But I am not such a parent. In your place, if there is pain, nurse it, and if there is a flame, don’t snuff it out, don’t be brutal with it. Withdrawal can be a terrible thing when it keeps us awake at night, and watching others forget us sooner than we’d want to be forgotten is no better. We rip out so much of ourselves to be cured of things faster than we should that we go bankrupt by the age of 30 and have less to offer each time we start with someone new. But to feel nothing so as not to feel anything—what a waste!”

The speech, in some regards, is wish-fulfillment for many gay people, who could only dream of being greeted with such unbridled love and understanding of who they are by their parents.

But while character types like “World’s Best Dad” or the “I Don’t Know How She Does It” mom have become stock clichés because of the ways the archetypes confuse parenting with infallible superheroism, it’s the quiet humanity and the casual gravity that Stuhlbarg lends Mr. Perlman that makes the character, and specifically that speech, so powerful.

“Forgive me if I have spoken out of turn,” Mr. Perlman tells Elio during that monologue. “I will have been a terrible father if, one day, you’d want to speak to me and felt the door was shut, or not sufficiently open.”

For all the film’s romance, that’s the moment that makes the audience swoon.

“All you can hope for is an opportunity to tell a story that seems to be what a lot of people have lived through, and perhaps present a different version of what it seems most people may have gone through in trying to communicate with a parent about who they are, what they feel, what their lives have been like,” Stuhlbarg told The Daily Beast during an interview last week before Call Me by Your Name hit theaters. “I’m grateful that people have expressed what they’re going through and what it meant to them. To be on the receiving end of it is breathtaking and humbling. Absolutely humbling.”

Michael Stuhlbarg is careful with his words, much in the same way that his Call Me by Your Name character is. Mr. Perlman recognizes the emotional intensity of the conversation he’s having with Elio, and wants to confirm that he isn’t speaking out of turn, anxious about upsetting his son in any way or betraying their delicate relationship.

As we speak, Stuhlbarg, too, seems sensitive to the fact that his film bears a lot of importance to a lot of people, and appears wary of misspeaking in a way that would rattle that moment or sully the film’s impact. He takes long pauses to consider how he wants to word things, speaking carefully, quietly, and deliberately, and politely confirming that he’s answered our questions. But he’s also careful not to articulate something too strongly so as to misrepresent his film and its message.

We bring up the tension, for example, that has seemed to follow the lead-up to Call Me by Your Name’s release, at least in terms of how the film is marketed and characterized in the press. It’s a film that obviously strikes a chord with a gay audience because it’s such a beautiful, rare depiction of a love story between two men. At the same time, the love story should be regarded as universal, regardless of the sexuality of the protagonists.

Thus there’s been some tangible hand-wringing over whether calling the film a gay love story will alienate some of its audience, or relegate it to a queer film ghetto of sorts, when it is a universal story that deserves a mainstream audience. Yet it is a gay story and the fact that it is a gay story matters. It’s a complicated conversation. What does Stuhlbarg make of the debate?

“Luca calls it a family story,” Stuhlbarg. “It’s as much about family as it is about those things. But, as you say, it’s coming at a unique time. I think one of the unique aspects of it is that there’s no real antagonist in the story other than time, the fact that these people who love each other don’t have a lot of time to spend together. At least in this situation they don’t.

“I think the language of how we talk about it is interesting,” he says. “I think people will come at it from their own unique perspectives and articulate it the way perhaps that they can at this moment. Maybe it will be the beginning of just articulating it as a love story as opposed to it being site-specific. But I also think it’s important to celebrate it for what it is from every perspective. Maybe it will start a dialogue at a time when we should be talking about it.”

Stuhlbarg is by no means resistant to talking about complex subject matters. As we wrote last week, he was diplomatic and gracious while discussing the cancellation of Gore, Netflix’s Gore Vidal biopic in which Stuhlbarg portrayed Vidal’s longtime lover, in the wake of allegations of sexual misconduct made against its star, Kevin Spacey. But he does become visibly more animated when we discuss the mechanics of making Call Me by Your Name, confirming suspicions that this is an actor more passionate about “the craft” than the noise that surrounds it.

We talk about whether he had any idea there would be such an intense reaction to his monologue. “I didn’t know,” he says. “My agent warned me. She said there’s a speech at the end of this that hit her hard. She said, ‘Wait, you’ll see.’”

We talk about grappling with how to even approach delivering a monologue as monumental as this one. It helped that the film was shot chronologically, he says, and that by that point he had grown close to Chalamet and Guadagnino. Plus, there were scenes that were shot detailing more of Mr. Perlman’s relationship with his wife and with his son that didn’t make the film’s final cut. “I was ready to let it be what it was going to be,” he says about the performing the monologue.

We talk about the mood on set the day the speech was filmed. “Intimate,” he says, with a long pause. “In the best way.”

But even though, at least to this reporter, he came off as rather shy and certainly humble while discussing his performance and its impact, he was still most eloquent when discussing just that. Even if, once again, he is careful about choosing those words.

“To birth a project that celebrates tolerance—not tolerance, forgive me—that celebrates compassion and tenderness, I’m all for that,” he says. “It’s a needed thing, I think, today in the stories that we share with each other. We could all do a whole lot of good by celebrating and sharing stories of closeness and intimacy and kindness [more] than necessarily just shooting things and blowing things up.”